Rembert’s resentments have been stoked by a barrage of attacks on TV and the stump by Mitt Romney and his allies accusing President Obama of eliminating the work requirements that were central to the nation’s 1996 tough welfare overhaul.

The trouble is, the charge is false.

The president in July opened the door for states to tinker with their individual welfare-to-work programs — a step Romney advocated for as Massachusetts governor in 2005 — but only if states show they will use that flexibility to improve, not lower, workforce participation rates. Independent experts and media fact-checking organizations confirmed this reading of Obama’s action.

The underlying sentiment of North Carolina Republicans like Rembert may explain why the Romney campaign continued for several weeks in August to air TV advertisements containing the allegation, despite the backlash. The idea that some poor families benefit by mooching off the system remains a potential source of white, middle-class anger.

Both campaigns have been fighting hard to win the backing of middle-class voters, whose economic fortunes have been squeezed over the last decade, with stagnant wages followed by the 2008 collapse in housing prices. Obama has sought to shore up support with the vast middle by issuing populist calls for tax increases on the wealthy and large corporations. Romney’s welfare effort appears intended to drive a wedge at the opposite end of the income scale, between the middle class and those who rely on expensive government services.

‘The ad is accurate. We simply disagree with the president’s policies and his decision to gut the bipartisan welfare reforms.’

The debate over the Romney tactics has touched on the third-rail subject of race. The Obama campaign has said it does not believe Romney’s welfare spots contain a racial subtext, and the Romney forces deny they are playing on racial divisions. The spots do not have any clear racial content, depicting a diverse workforce toiling in factories, and images of the president with a voiceover that says he gutted the work requirement.

Nonetheless, the ads have drawn accusations from analysts and others that the former Massachusetts governor is subtly exploiting longstanding perceptions about welfare and race in America.

“It’s like Willie Horton redux,’’ said Larry Rasky, a Boston political communications specialist and former campaign aide to vice president Joe Biden. Advertisements highlighting Horton, an African-American convict furloughed from a Massachusetts prison who later committed rape, were successfully used by President George H.W. Bush against Michael Dukakis, former Bay State governor, in 1988.

The Rev. Jesse Jackson said in an interview in Charlotte last week that Romney’s ads contained an unspoken, racial subtext.

“It is a dog-whistle. It’s part of a whole orchestra of whistles — you’re a liar, you’re not American, you’re not legitimate. It’s all part of the same symphony,’’ Jackson said.

The Romney campaign, without offering a specific explanation, stood by the veracity of its advertisements.

“The ad is accurate,’’ spokesman Ryan Williams said in a statement to the Globe. “We simply disagree with the president’s policies and his decision to gut the bipartisan welfare reforms signed into law by President Clinton.’’

The spot did not appear to be airing in North Carolina and other states during the two weeks of the conventions. Williams did not say when or if the Romney campaign would put it back on. Romney, his vice presidential nominee, Paul Ryan, Newt Gingrich, Rick Santorum, and other GOP figures have repeated the charge in recent weeks in interviews, on the stump, and at their convention in Tampa. The issue is picking up steam in Congress, where Republicans are seeking to force a vote to block states from gaining the flexibility Obama has authorized.

In an interview with USA Today, Romney in August asserted his campaign advertising was accurate. He accused Obama of loosening welfare work requirements to “shore up his base.’’

Voter dissatisfaction over social welfare programs has sometimes been the subject of political campaigns. President Reagan, for instance, tapped into such sentiment when he targeted a stereotypical “welfare queen’’ in an unsuccessful primary campaign for president in 1976.

President Clinton — who rebutted the Romney charge as false and “a real doozy’’ in his Democratic National Convention speech last Wednesday — forged the bipartisan compromise with Congress in 1996 that resulted in a completely revamped program, with minimum hourly work requirements for able-bodied welfare recipients and lifetime caps on benefits. Welfare rolls in America today contain about equal numbers of African-Americans and whites.

Over the years, states have sought greater flexibility to manage their welfare-to-work efforts. In 2005, as Congress was working to renew the welfare bill, the Republican Governors Association urged Congress to build in that flexibility in the form of “waivers.’’

“Increased waiver authority, allowable work activities, availability of partial-work credit, and the ability to coordinate state programs are all important aspects of moving recipients from welfare to work,’’ the governors wrote.

Romney, then in his third year as governor, was among the 30 Republican governors who signed the letter. At the time, the Romney administration was seeking flexibility to make more education and training programs count toward minimum work requirements, said a member of a welfare advisory committee.

“We felt we had a better mousetrap,’’ said the panelist, Jeffrey Hayward, chief of external affairs at the United Way of Massachusetts. “We thought we could save money; we could get more people off welfare.’’

Williams denied, despite the wording of the 2005 Republican Governors Association letter, that the Republican governors supported flexibility in work rules. They were “not requesting waivers from core work requirements,’’ he said.

The National Conference of State Legislatures — a bipartisan organization in Denver that provides research and technical assistance to lawmakers in 50 states — said it is clear that waiving work requirements was not the intent of the Obama administration’s effort.

“They want to give states more flexibility so they can develop more effective approaches,’’ said Jack Tweedie, a social services programs analyst at the conference. “States will want to figure out how to move recipients into work.’’

But the day after the Obama administration said in July it would grant states flexibility they had been seeking, the conservative Heritage Foundation, a Washington think-tank, posted a blog that began, “The imperial presidency has overturned Congress and the law again.’’

Within a month, Romney had seized on the argument: “They just send you your welfare check. And welfare-to-work goes back to being plain old welfare,’’ said the campaign’s ad.

A supporter of the administration’s policy, Elizabeth O. Ananat, a Duke University associate professor of public policy and economics who spent a brief time as an Obama economic adviser, said she was dismayed by the TV spot. “It’s really disappointing to me to use something that has been a bipartisan success,’’ she said, “as an election-year cudgel.’’